Supplementary Angles That Are Not A Linear Pair

     My grandparents' house has a small roof over the front porch. The two parallel lines are formed by one side of the main house and another side of the jutting out part. The line along the porch roof is a transversal to those two parallel lines. Because of consecutive interior angles, we know that angle one and angle two are nonadjacent supplementary angles. Architecturally, the two parallel lines are parallel because they have to both be perpendicular to the ground in order for the house to stand. The line along the small roof has to protect the porch and let water drip from it, thus allowing it to be slanted and not perpendicular to the parallel lines. Many objects in the real world have two parallel lines cut by a transversal, such as window frames, but those have 90 degree angles. My picture/example of nonadjacent supplementary angles is unique, as angles one and two are not congruent.     

Non-congruent Alternate Interior Angles

      This is the railing beside the stairs on the outside of my grandparents’ house that has many vertical poles, one diagonal pole, and horizontal poles holding everything together. The vertical pole acts as the transversal to the diagonal and horizontal poles. And because these two poles are not parallel, the alternate interior angles are not congruent. Many houses have a railing leading up to their front door, so the horizontal and vertical poles (that are perpendicular) provide support for it to stand up straight. But, the diagonal pole, in the picture below, acts as a hand rail and extra support for the railing itself. Almost any building or house in the world that has stairs, uses a railing for support and safety reasons. It is especially helpful that the diagonal pole and the horizontal pole do not provide alternate interior angles because people need a stronger support system to grab when walking up stairs or an incline. And non-parallel lines give a structure something diferent and sometimes stronger to work with.